You start somewhere in the hold of a ship that has docked at the village of Seyda Neen in the Vvardenfell province of Morrowind. Your characteristics will be generated as you go along. The character generation process is integrated into the storyline and provides a quick tutorial on how do basic game functions (moving, talking, picking things up, etc). Just follow the directions (not that you can do anything except follow the directions).
The ship that brings you to Vvardenfell will disappear as soon as you step into the Excise and Census office. There isn't anything that you can do to or on it, so we'll just ignore it and pick up with the point where you CAN have an effect on your world.
Talk to Socucius Ergalla (he's the fellow in the robe directly in front of you). His stats: level 14 Agent, 102 HP, 128 MP, Steel Shardblade (and he knows how to use it -- 54% Short Blade skill), a few golds. You will set up your class with him. He will have a small side quest for you a bit later on and he is also available for training (Speechcraft, Short Blade, Light Armor -- all 54%). It might be worthwhile to leave him in peace for now.
Take your release papers to Sellus Gravius in the next building. Gravius is a level 17 Guard, 186 HP, Templar Armor, Imperial Broadsword (with a 69% skill to go with it). Click on "duties" to get a package of papers for Caius Cosades in Balmora.
The directions tell you not to break the seal on the package, but I don't find any of Cosades' dialogue options that indicate a broken seal, so reading it probably won't hurt. But just in case, click here to see what it says (fat lot of good it will do you, unless you are good at working those cryptoquote puzzles - it's a letter substitution cypher).
On the way to the next building, feel free to plunder whatever you can lay your hands on (I'd leave the stuff in the front office alone unless you've managed to come up with some serious Sneak and Security skills in the last 5 minutes). Aside from a Dagger, a few golds and an Apprentice's Lockpick, there isn't much of value in the buildings, but you will probably need the money you'll get from selling it. There is a magic ring (minor Healing) in the barrel beside the door of Gravius' building. Grab it (actually, you'll get a popup warning telling you to grab it). You will need it to complete a side quest, but it's also a fairly harmless way to get a feel for spellcasting.
Once you have finished with the good captain and step out the front door into Seyda Neen, you're on your own (and the game tells you so). Aren't you glad you've got this walkthru to help you through the rough spots?
Before you go any farther, take a moment to read the page about restraining yourself. It will make your life so much easier.